When considering the relationship between student makeup and the instrument Panel B, I found none to be statistically significant.
In summary, statistically significant correlations exist between some motherhood characteristics and the share of students who are black when considering the 1981–
83 birth cohort. There may be unobservable factors also correlated with pollution that bias OLS regressions. There are no economically significant correlations be-
tween my instrument for pollution and any observable mother or student character- istics, and the use of the instrumental variables strategy may alleviate concerns over
unobservables.
V. Econometric model
I collapse all student data by demographic group, school of atten- dance, year of birth, and year of test to limit potential omitted variables bias caused
by higher levels of aggregation see Hanushek, Rivkin, and Taylor 1996. I weight all regressions by the number of students in each cell.
12
The OLS estimation model is:
y = βTSP
+ α + θ + δX + ωB
+ ψT + γW
+ ε ,
3
s,b,t c,b
s b,t
s,t c,b
c,t c,b
s,b,t
where s, c, b, and t refer to school, county, year of birth, and year of the test, respectively. The parameter β is the estimated achievement impact of an additional
unit of TSP exposure in the child’s year of birth, α
s
is a vector of school fixed effects, θ
b,t
is a vector of year of birth by year of test fixed effects, X
s,t
is a vector of collapsed individual school-level student and school covariates, B
c,b
is a vector of economic and demographic covariates in the year of birth, T
c,t
is a vector of economic and demographic covariates in the year of the test, W
c,b
is a vector of county-level weather covariates in the year of birth, and ε is an error term. Pollution
treatment varies at the county by year of birth level. In my IV analysis, I model TSPs as a function of all workers in a county employed
in the manufacturing industry SIC code 400 over total county employment levels in all other sectors in a given year. Given a linear relationship where Π is defined
as the marginal impact of changes in relative manufacturing employment, the rela- tionship minus other covariates is:
manufacturing
c,t
TSP = Π
∗100 4
c,t
all −manufacturing
c,t c,t
I multiply the result by 100 to make Π interpretable as a percentage change. Clearly, controlling for income is important. The recession was likely accompanied by loss
of income, which could in turn have an impact on fetal health and long-run cognitive growth. But income is likely to be correlated with the error term in the regression
of pollution on test scores. I instrument for per capita income using changes in
12. For example, one cell would be nonspecial education white students on free lunch at school s born in year b taking the exam in year t.
national crude oil prices and the strong link between crude oil prices and income in Texas.
13
I theorize counties with larger oil extraction sectors prior to the recession had their per capita incomes change more drastically with crude oil prices similar
to the coal reserves and county wages instrument used in Black, Daniel, and Sanders 2002. Due to the limited availability of specific oil extraction employment, I use
the more general mining employment SIC code 200, which contains within it petroleum extraction, drilling, and other oil-mining employment sources. My final
income instrument is the annual inflation-adjusted price of crude oil weighted by the fraction of county employment in the mining and extraction industry prior to
the recession using an average of 1976–78 values as the baseline:
mining
c,baseline
income = oil price ∗
5
c,t
all −mining
c,baseline c,baseline
While annual crude oil price variation occurs on the national level, the instrument varies by county due to the cross-county differences in prerecession mining sector
size.
VI. Results
